I wouldn't use "entonces" in these cases. "Así que" sounds perfect. You'll usually want to use "entonces" as an equivalent for the English "then".

Hm... We would probably say the whole sentence different in Spanish: Estaba con frio porque me habia olvidado la campera (I was cold cause I had forgotten my jacket). Still, as you say it in your example, I would translate -> Y por esto. So can be translated in many different ways... it really depends on the context. Some examples: por lo tanto por lo cual así tan tanto de este modo de esta manera por tanto por consiguiente

-"por lo que" -"y es por eso que"

Or "y por esa razón"

I would use "así que".